Adding and Subtracting Fractions and Mixed Numbers

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.

A mixed number is a whole number combined with a fraction. For example, 2 1/2 is a mixed number, which means 2 whole parts and 1/2 of another part.

To add fractions with the same denominator, keep the denominator the same and add the numerators. For example, $$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$$ .

To subtract fractions with the same denominator, keep the denominator the same and subtract the numerators. For example, $$\frac{3}{5} - \frac{1}{5} = \frac{2}{5}$$ .

When adding fractions with different denominators, first find a common denominator, convert the fractions, and then add the numerators. For example, to add $$\frac{1}{3} + \frac{1}{4}$$ , the common denominator is 12, so it becomes $$\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$$ .

The first step in subtracting mixed numbers is to convert them into improper fractions. For example, to subtract 2 1/2 from 3 3/4, convert both to improper fractions: 2 1/2 = $$\frac{5}{2}$$ and 3 3/4 = $$\frac{15}{4}$$ .

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. For example, for 2 1/3, it becomes $$\frac{2 \times 3 + 1}{3} = \frac{7}{3}$$ .

The result of $$\frac{3}{12} + \frac{4}{12}$$ is $$\frac{7}{12}$$ .

The result of $$\frac{16}{12} - \frac{4}{12}$$ is $$\frac{12}{12} = 1$$ .

The result of $$1 \frac{5}{12} - \frac{4}{12}$$ is $$1 \frac{1}{12}$$ .